Parameter identification with weightless regularization

Although the regularization increased the popularity of parameter identification due to its capability of deriving a stable solution, the significant problem is that the solution depends upon the regularization parameters chosen. This paper presents a technique for deriving solutions without the use of the parameters and, further, an optimization method, which can work efficiently for problems of concern. Numerical examples show that the technique can efficiently search for appropriate solutions. Copyright © 2001 John Wiley & Sons, Ltd.

[1]  T. Brubaker,et al.  Nonlinear Parameter Estimation , 1979 .

[2]  Thomas Bäck,et al.  Genetic Algorithms and Evolution Strategies - Similarities and Differences , 1990, PPSN.

[3]  J. Baumeister.  Stable solution of inverse problems , 1987 .

[4]  Genki Yagawa,et al.  INELASTIC CONSTITUTIVE PARAMETER IDENTIFICATION USING AN EVOLUTIONARY ALGORITHM WITH CONTINUOUS INDIVIDUALS , 1997 .

[5]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[6]  Carl August Zehnder,et al.  Numerical methods of mathematical optimization , 1971 .

[7]  Teresa Reginska,et al.  A Regularization Parameter in Discrete Ill-Posed Problems , 1996, SIAM J. Sci. Comput..

[8]  An efficient numerical algorithm with adaptive regularization for parameter estimations , 1998 .

[9]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[10]  Takashi Kitagawa.  A Numerical Method to Estimate the Optimal Regularization Parameter , 1989 .

[11]  Thomas Bäck,et al.  An Overview of Evolutionary Algorithms for Parameter Optimization , 1993, Evolutionary Computation.

[12]  Genki Yagawa,et al.  Implicit constitutive modelling for viscoplasticity using neural networks , 1998 .

[13]  C. W. Groetsch,et al.  The theory of Tikhonov regularization for Fredholm equations of the first kind , 1984 .

[14]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[15]  William H. Press,et al.  Numerical recipes in C , 2002 .

[16]  Genki Yagawa,et al.  An extensible evolutionary algorithm approach for inverse problems , 1998 .

[17]  Kenneth Alan De Jong,et al.  An analysis of the behavior of a class of genetic adaptive systems. , 1975 .

[18]  T. Kitagawa.  A deterministic approach to optimal regularization —The finite dimensional case— , 1987 .

[19]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[20]  Y. Honjo,et al.  Matching objective and subjective information in geotechnical inverse analysis based on entrophy minimization , 1998 .

[21]  V. A. Morozov,et al.  Methods for Solving Incorrectly Posed Problems , 1984 .

[22]  Hans-Paul Schwefel,et al.  Numerical Optimization of Computer Models , 1982 .

[23]  Shiro Kubo,et al.  Characterization of the Tikhonov regularization for numerical analysis of inverse boundary value problems by using the singular value decomposition , 1998 .

[24]  Genki Yagawa,et al.  Genetic Algorithms for Real Search Space and Their Use for Nonlinear Inverse Problems. , 1995 .

[25]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .